In the section of the movie where the refugees travel to the US, there is a scene that shows a Delta Aircraft (767-300ER) landing. The livery shown on the aircraft is the current livery used from 2008-present, also known as the "Upward and Onward" scheme, changed because of the merger with Northwest Airlines. The time that the refugees would have been traveling to the US is before the merger, so that livery should not have been used. The proper livery would be the either the "Colors in Motion" scheme, used from 2000 until the merger with Northwest Airlines, or the Ron Allen scheme, which was the livery used before 2000.
When the refugees first arrive in Kansas City and mention needing to meet an escort by the baggage claim, they descend an escalator. MCI (Kansas City's primary airport) does not have a lower level baggage claim. The airport is three, single-level terminals all with various baggage claims on the same level.